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Roy Fleming (Don Knotts) is fairground operator of a kiddie-spaceship ride. Despite being thirty-five years old, he still lives with his parents and suffers from extreme acrophobia (fear of heights). His father Arbuckle (Arthur O'Connell) wants better things for his son, so he sends an application to NASA. Roy later learns from his mother (Jeanette Nolan) that NASA has accepted him as a "WB-1074".
When Roy arrives at the Manned Spacecraft Center in Houston, supervisor Donelli (Jesse White) places him in training as a janitor. Roy accepts the disappointment and unsuccessfully tries to explain things to his family back home, who believe that he is an astronaut. Meanwhile, he is befriended by veteran astronaut Major Fred Gifford (Leslie Nielsen). One day, Roy is alarmed to discover that his father and his friends, Plank (Frank McGrath) and Rush (Paul Hartman) are paying him a surprise visit at work. Anxious to please his domineering father, he dons a space suit and pretends to be an astronaut. Arbuckle a World War I veteran, tells his friends, "he is proud Roy is now serving his nation." After wreaking general havoc on the simulators and other hardware, Roy is exposed as a janitor by Donelli and summarily fired in the presence of his father.
When the Russians plan to trump NASA by sending a dentist into space, NASA moves quickly. Roy is found in a bar, rehired, and selected as the man least likely to venture into space and sent aloft. His father watches on TV, convinced the janitor story was a ploy for security reasons. During some eating experiments, Roy gets peanut butter into the guidance system and is in danger of being marooned in space. He remembers the retro rockets from his role as "Mr. Spaceman" on the amusement park ride and launches them, bringing the capsule safely home. Roy is hailed as a hero, and marries his sweetheart Ellie Jackson (Joan Freeman).